Zeitschriftenartikel: „Nelder-Mead algoritmus“

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Lewis, Andrew, David Abramson und Tom Peachey. „RSCS: A Parallel Simplex Algorithm for the Nimrod/O Optimization Toolset“. Scientific Programming 14, Nr. 1 (2006): 1–11. http://dx.doi.org/10.1155/2006/906394.

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This paper describes a method of parallelisation of the popular Nelder-Mead simplex optimization algorithms that can lead to enhanced performance on parallel and distributed computing resources. A reducing set of simplex vertices are used to derive search directions generally closely aligned with the local gradient. When tested on a range of problems drawn from real-world applications in science and engineering, this reducing set concurrent simplex (RSCS) variant of the Nelder-Mead algorithm compared favourably with the original algorithm, and also with the inherently parallel multidirectional search algorithm (MDS). All algorithms were implemented and tested in a general-purpose, grid-enabled optimization toolset.

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Kshirsagar, Rohit, Steve Jones, Jonathan Lawrence und Jim Tabor. „Optimization of TIG Welding Parameters Using a Hybrid Nelder Mead-Evolutionary Algorithms Method“. Journal of Manufacturing and Materials Processing 4, Nr. 1 (10.02.2020): 10. http://dx.doi.org/10.3390/jmmp4010010.

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A number of evolutionary algorithms such as genetic algorithms, simulated annealing, particle swarm optimization, etc., have been used by researchers in order to optimize different manufacturing processes. In many cases these algorithms are either incapable of reaching global minimum or the time and computational effort (function evaluations) required makes the application of these algorithms impractical. However, if the Nelder Mead optimization method is applied to approximate solutions cheaply obtained from these algorithms, the solution can be further refined to obtain near global minimum of a given error function within only a few additional function evaluations. The initial solutions (vertices) required for the application of Nelder-Mead optimization can be obtained through multiple evolutionary algorithms. The results obtained using this hybrid method are better than that obtained from individual algorithms and also show a significant reduction in the computation effort.

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Pošík, Petr, und Waltraud Huyer. „Restarted Local Search Algorithms for Continuous Black Box Optimization“. Evolutionary Computation 20, Nr. 4 (Dezember 2012): 575–607. http://dx.doi.org/10.1162/evco_a_00087.

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Several local search algorithms for real-valued domains (axis parallel line search, Nelder-Mead simplex search, Rosenbrock's algorithm, quasi-Newton method, NEWUOA, and VXQR) are described and thoroughly compared in this article, embedding them in a multi-start method. Their comparison aims (1) to help the researchers from the evolutionary community to choose the right opponent for their algorithm (to choose an opponent that would constitute a hard-to-beat baseline algorithm), (2) to describe individual features of these algorithms and show how they influence the algorithm on different problems, and (3) to provide inspiration for the hybridization of evolutionary algorithms with these local optimizers. The recently proposed Comparing Continuous Optimizers (COCO) methodology was adopted as the basis for the comparison. The results show that in low dimensional spaces, the old method of Nelder and Mead is still the most successful among those compared, while in spaces of higher dimensions, it is better to choose an algorithm based on quadratic modeling, such as NEWUOA or a quasi-Newton method.

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Ali, Ahmed F., und Mohamed A. Tawhid. „Direct Gravitational Search Algorithm for Global Optimisation Problems“. East Asian Journal on Applied Mathematics 6, Nr. 3 (20.07.2016): 290–313. http://dx.doi.org/10.4208/eajam.030915.210416a.

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AbstractA gravitational search algorithm (GSA) is a meta-heuristic development that is modelled on the Newtonian law of gravity and mass interaction. Here we propose a new hybrid algorithm called the Direct Gravitational Search Algorithm (DGSA), which combines a GSA that can perform a wide exploration and deep exploitation with the Nelder-Mead method, as a promising direct method capable of an intensification search. The main drawback of a meta-heuristic algorithm is slow convergence, but in our DGSA the standard GSA is run for a number of iterations before the best solution obtained is passed to the Nelder-Mead method to refine it and avoid running iterations that provide negligible further improvement. We test the DGSA on 7 benchmark integer functions and 10 benchmark minimax functions to compare the performance against 9 other algorithms, and the numerical results show the optimal or near optimal solution is obtained faster.

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Kumar K, Pavan, Murali Mohan J und Srikanth D. „Generalized solution for inverse kinematics problem of a robot using hybrid genetic algorithms“. International Journal of Engineering & Technology 7, Nr. 4.6 (25.09.2018): 250. http://dx.doi.org/10.14419/ijet.v7i4.6.20486.

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The robot control consists of kinematic control and dynamic control. Control methods of the robot involve forward kinematics and inverse kinematics (IK). In Inverse kinematics the joint angles are found for a given position and orientation of the end effector. Inverse kinematics is a nonlinear problem and has multiple solutions. This computation is required to control the robot arms. A Genetic Algorithm (GA) and Hybrid genetic algorithm (HGA) (Genetic Algorithm in conjunction with Nelder-Mead technique) are proposed for solving the inverse kinematics of a robotic arm. HGA introduces two concepts exploration, exploitation. In an exploration phase, the GA identifies the good areas in entire search space and then exploitation phase is performed inside these areas by using Nelder- mead technique Binary Simulated Crossover and niching strategy for binary tournament selection operator is used. Proposed algorithms can be used on any type of manipulator and the only requirement is the forward kinematic equations, which are easily obtained. As a case study inverse kinematics of a Two Link Elbow Manipulator and PUMA manipulator are solved using GA and HGA in MATLAB. The algorithm is able to find all solutions without any error

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Papliński, Janusz P. „Hybrid Genetic and Nelder-Mead Algorithms for Identification of Time Delays“. IFAC Proceedings Volumes 42, Nr. 13 (2009): 443–48. http://dx.doi.org/10.3182/20090819-3-pl-3002.00077.

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Ahandani, Morteza Alinia, und Hosein Alavi-Rad. „Hybridizing Shuffled Frog Leaping and Shuffled Complex Evolution Algorithms Using Local Search Methods“. International Journal of Applied Evolutionary Computation 5, Nr. 1 (Januar 2014): 30–51. http://dx.doi.org/10.4018/ijaec.2014010103.

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In this research, a study was carried out to exploit the hybrid schemes combining two classical local search techniques i.e. Nelder–Mead simplex search method and bidirectional random optimization with two meta-heuristic methods i.e. the shuffled frog leaping and the shuffled complex evolution, respectively. In this hybrid methodology, each subset of meta-heuristic algorithms is improved by a hybrid strategy that is combined from evolutionary process of each subset in related algorithm and a local search method. These hybrid algorithms are evaluated on low and high dimensional continuous benchmark functions and the obtained results are compared with their non-hybrid competitors. The obtained results demonstrate that the hybrid algorithm combined from shuffled frog leaping and Nelder–Mead simplex has a better success rate but a higher number of function evaluations on low-dimensional functions than the shuffled frog leaping. Whereas on high-dimensional functions it has a better success rate and a faster performance. Also the hybrid algorithm combined from shuffled complex evolution and bidirectional random optimization obtains a better performance in terms of success rate and function evaluations than shuffled complex evolution on low dimensional functions; whereas on high-dimensional functions, it obtains a better success rate but a slower performance. Also a comparison of our hybrid algorithms with the other evolutionary algorithms reported in the literature confirms our proposed algorithms have the best performance among all compared algorithms.

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Santhosh, M., und P. Sudhakar. „Nelder Mead with Grasshopper Optimization Algorithm for Node Localization in Wireless Sensor Networks“. Journal of Computational and Theoretical Nanoscience 17, Nr. 12 (01.12.2020): 5409–21. http://dx.doi.org/10.1166/jctn.2020.9434.

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Node localization in wireless sensor network (WSN) becomes essential to calculate the coordinate points of the unknown nodes with the use of known or anchor nodes. The efficiency of the WSN has significant impact on localization accuracy. Node localization can be considered as an optimization problem and bioinspired algorithms finds useful to solve it. This paper introduces a novel Nelder Mead with Grasshopper Optimization Algorithm (NMGOA) for node localization in WSN. The Nelder-Mead simplex search method is employed to improve the effectiveness of GOA because of its capability of faster convergence. At the beginning, the nodes in WSN are arbitrarily placed in the target area and then nodes are initialized. Afterwards, the node executes the NMGOA technique for estimating the location of the unknown nodes and become localized nodes. In the subsequent round, the localized nodes will be included to the collection of anchor nodes to perform the localization process. The effectiveness of the NMGOA model is validated using a series of experiments and results indicated that the NMGOA model has achieved superior results over the compared methods.

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Negrin, Iván A., Alejandro Negrin und Ernesto L. Chagoyén. „Optimización de pórticos planos de hormigón armado utilizando una hibridación de algoritmos genéticos y el algoritmo Nelder-Mead“. Obras y proyectos, Nr. 26 (Dezember 2019): 74–86. http://dx.doi.org/10.4067/s0718-28132019000200074.

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Kriauzienė, Rima, Andrej Bugajev und Raimondas Čiegis. „A THREE-LEVEL PARALLELISATION SCHEME AND APPLICATION TO THE NELDER-MEAD ALGORITHM“. Mathematical Modelling and Analysis 25, Nr. 4 (13.10.2020): 584–607. http://dx.doi.org/10.3846/mma.2020.12139.

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We consider a three-level parallelisation scheme. The second and third levels define a classical two-level parallelisation scheme and some load balancing algorithm is used to distribute tasks among processes. It is well-known that for many applications the efficiency of parallel algorithms of these two levels starts to drop down after some critical parallelisation degree is reached. This weakness of the twolevel template is addressed by introduction of one additional parallelisation level. s an alternative to the basic solver some new or modified algorithms are considered on this level. The idea of the proposed methodology is to increase the parallelisation degree by using possibly less efficient algorithms in comparison with the basic solver. As an example we investigate two modified Nelder-Mead methods. For the selected application, a Schro¨dinger equation is solved numerically on the second level, and on the third level the parallel Wang’s algorithm is used to solve systems of linear equations with tridiagonal matrices. A greedy workload balancing heuristic is proposed, which is oriented to the case of a large number of available processors. The complexity estimates of the computational tasks are model-based, i.e. they use empirical computational data.

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Pholdee, Nantiwat, Vivek K. Patel, Sadiq M. Sait, Sujin Bureerat und Ali Rıza Yıldız. „Hybrid spotted hyena–Nelder-Mead optimization algorithm for selection of optimal machining parameters in grinding operations“. Materials Testing 63, Nr. 3 (01.03.2021): 293–98. http://dx.doi.org/10.1515/mt-2020-0043.

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Abstract In this research, a novel optimization algorithm, which is a hybrid spotted hyena-Nelder-Mead optimization algorithm (HSHO-NM) algorithm, has been introduced in solving grinding optimization problems. A well-known grinding optimization problem is solved to prove the superiority of the HSHO-NM over other algorithms. The results of the HSHO-NM are compared with others. The results show that HSHO-NM is an efficient optimization approach for obtaining the optimal manufacturing variables in grinding operations.

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Dewi, Yuliani S., Purhadi, Sutikno und Santi W. Purnami. „Comparison of Nelder Mead and BFGS Algorithms on Geographically Weighted Multivariate Negative Binomial“. International Journal on Advanced Science, Engineering and Information Technology 9, Nr. 3 (26.05.2019): 979. http://dx.doi.org/10.18517/ijaseit.9.3.6932.

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Liu, Xin Liang, Tao Yin und Guo Dong Wu. „Practical Application Study of Gaussian Process Model in Construction Project Cost Estimation“. Advanced Materials Research 671-674 (März 2013): 3100–3106. http://dx.doi.org/10.4028/www.scientific.net/amr.671-674.3100.

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Early understanding of construction cost represents a critical factor of a feasibility study in the early design phase of a project. A new project cost estimation model based on Gaussian Process was proposed. Gaussian Process model theory was introduced, and project cost estimation model based on Gaussian Process’ flow chart was analyzed in detail. Through example analysis, project cost estimation model based on Gaussian Process using Nelder-Mead and genetic algorithms algorithm was proven feasible for this problem and represented accuracy than BP neural network.

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Pošík, Petr, und Jiří Kubalík. „Experimental Comparison of Six Population-Based Algorithms for Continuous Black Box Optimization“. Evolutionary Computation 20, Nr. 4 (Dezember 2012): 483–508. http://dx.doi.org/10.1162/evco_a_00083.

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Six population-based methods for real-valued black box optimization are thoroughly compared in this article. One of them, Nelder-Mead simplex search, is rather old, but still a popular technique of direct search. The remaining five (POEMS, G3PCX, Cauchy EDA, BIPOP-CMA-ES, and CMA-ES) are more recent and came from the evolutionary computation community. The recently proposed comparing continuous optimizers (COCO) methodology was adopted as the basis for the comparison. The results show that BIPOP-CMA-ES reaches the highest success rates and is often also quite fast. The results of the remaining algorithms are mixed, but Cauchy EDA and POEMS are usually slow.

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Gumier, Carlos César, und Edevar Luvizotto Junior. „Aplicação de modelo de simulação-otimização na gestão de perda de água em sistemas de abastecimento“. Engenharia Sanitaria e Ambiental 12, Nr. 1 (März 2007): 32–41. http://dx.doi.org/10.1590/s1413-41522007000100005.

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Este artigo apresenta a aplicação de modelo matemático-computacional de simulação e otimização para localização de fugas. O modelo proposto é fundamentado no acoplamento de um simulador hidráulico baseado no Time Marching Approach - TMA com o algoritmo otimizador de Nelder-Mead e foi aplicado em uma rede de distribuição de água da cidade de Jundiaí-SP. Nos testes realizados ficou claro o funcionamento adequado do modelo apresentado, pois a fuga simulada foi localizada, sendo observado, entretanto, a necessidade de um aprimoramento na localização dos pontos de monitoramento durante a execução da simulação.

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Boukhari, Noureddine, Fatima Debbat, Nicolas Monmarché und Mohamed Slimane. „Solving Mono- and Multi-Objective Problems Using Hybrid Evolutionary Algorithms and Nelder-Mead Method“. International Journal of Applied Metaheuristic Computing 12, Nr. 4 (Oktober 2021): 98–116. http://dx.doi.org/10.4018/ijamc.2021100106.

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Evolution strategies (ES) are a family of strong stochastic methods for global optimization and have proved their capability in avoiding local optima more than other optimization methods. Many researchers have investigated different versions of the original evolution strategy with good results in a variety of optimization problems. However, the convergence rate of the algorithm to the global optimum stays asymptotic. In order to accelerate the convergence rate, a hybrid approach is proposed using the nonlinear simplex method (Nelder-Mead) and an adaptive scheme to control the local search application, and the authors demonstrate that such combination yields significantly better convergence. The new proposed method has been tested on 15 complex benchmark functions and applied to the bi-objective portfolio optimization problem and compared with other state-of-the-art techniques. Experimental results show that the performance is improved by this hybridization in terms of solution eminence and strong convergence.

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Nahlik, Jiri, Jiri Hospodka, Pavel Sovka, Brendan Mullane und Ondrej Subrt. „Performance optimization methods for switched-capacitor biquadratic filters“. Journal of Electrical Engineering 69, Nr. 5 (01.09.2018): 345–51. http://dx.doi.org/10.2478/jee-2018-0050.

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Abstract A class of computer-aided optimization methods based on Differential Evolution (DE), Particle Swarm Optimization (PSO) and Nelder Mead algorithms applied to a switched-capacitor (SC) filter circuit design are investigated. Comparisons of these algorithms applied to a 4th order biquadratic two-channel filter bank CMOS design on 0.35 µm technology are made. The frequency responses of the biquadratic filters must match ideal responses in a finite number of iterations with a limited number of “particles”. The original and derived methods are evaluated on the base of their convergence progress and their reliability over different starting populations. An optimal design approach based on combining algorithms is derived as a more suitable and more reliable method for SC circuit optimization.

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Baulac, Marine, Jérôme Defrance und Philippe Jean. „Optimization of multiple edge barriers with genetic algorithms coupled with a Nelder–Mead local search“. Journal of Sound and Vibration 300, Nr. 1-2 (Februar 2007): 71–87. http://dx.doi.org/10.1016/j.jsv.2006.07.030.

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Goryainov, V. B., und W. M. Khing. „Comparison of Classical and Robust Estimates of Threshold Auto-regression Parameters“. Mathematics and Mathematical Modeling, Nr. 5 (06.02.2021): 33–44. http://dx.doi.org/10.24108/mathm.0520.0000224.

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The exponential auto-regression model is a discrete analog of the second-order nonlinear differential equations of the type of Duffing and van der Pol oscillators. It is used to describe nonlinear stochastic processes with discrete time, such as vehicle vibrations, ship roll, electrical signals in the cerebral cortex. When applying the model in practice, one of the important tasks is its identification, in particular, an estimate of the model parameters from observations of the stochastic process it described. A traditional technique to estimate autoregressive parameters is the nonlinear least squares method. Its disadvantage is high sensitivity to the measurement errors of the process observed. The M-estimate method largely has no such a drawback. The M-estimates are based on the minimization procedure of a non-convex function of several variables. The paper studies the effectiveness of several well-known minimization methods to find the M-estimates of the parameters of an exponential autoregressive model. The paper demonstrates that the sequential quadratic programming algorithm, the active set algorithm, and the interior-point algorithm have shown the best and approximately the same accuracy. The quasi-Newton algorithm is inferior to them in accuracy a little bit, but is not inferior in time. These algorithms had approximately the same speed and were one and a half times faster than the Nelder-Mead algorithm and 14 times faster than the genetic algorithm. The Nelder-Mead algorithm and the genetic algorithm have shown the worst accuracy. It was found that all the algorithms are sensitive to initial conditions. The estimate of parameters, on which the autoregressive equation linearly depends, is by an order of magnitude more accurate than that of the parameter on which the auto-regression equation depends in a nonlinear way.

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Khoja, Intissar, Taoufik Ladhari, Faouzi M’sahli und Anis Sakly. „Cuckoo Search Approach for Parameter Identification of an Activated Sludge Process“. Computational Intelligence and Neuroscience 2018 (2018): 1–9. http://dx.doi.org/10.1155/2018/3476851.

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A parameter identification problem for a hybrid model is presented. The latter describes the operation of an activated sludge process used for waste water treatment. Parameter identification problem can be considered as an optimization one by minimizing the error between simulation and experimental data. One of the new and promising metaheuristic methods for solving similar mathematical problem is Cuckoo Search Algorithm. It is inspired by the parasitic brood behavior of cuckoo species. To confirm the effectiveness and the efficiency of the proposed algorithm, simulation results will be compared with other algorithms, firstly, with a classical method which is the Nelder-Mead algorithm and, secondly, with intelligent methods such as Genetic Algorithm and Particle Swarm Optimization approaches.

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Kheireddine, Bourahla, Belli Zoubida und Hacib Tarik. „Improvements of bat algorithm using crossover technique and hybridization with Nelder-Mead simplex method“. COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 38, Nr. 3 (07.05.2019): 977–89. http://dx.doi.org/10.1108/compel-09-2018-0374.

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Purpose This study aims to improve the bat algorithm (BA) performance for solving optimization problems in electrical engineering. Design/methodology/approach For this task, two strategies were investigated. The first one is based on including the crossover technique into classical BA, in the same manner as in the genetic algorithm method. Therefore, the newly generated version of BA is called the crossover–bat algorithm (C-BA). In the second strategy, a hybridization of the BA with the Nelder–Mead (NM) simplex method was performed; it gives the NM-BA algorithm. Findings First, the proposed strategies were applied to solve a set of two standard benchmark problems; then, they were applied to solve the TEAM workshop problem 25, where an electromagnetic field was computed by use of the 2D non-linear finite element method. Both optimization algorithms and finite element computation tool were implemented under MATLAB. Originality/value The two proposed optimization strategies, C-BA and NM-BA, have allowed good improvements of classical BA, generally known for its poor solution quality and slow convergence rate.

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Rosić, Maja B., Mirjana I. Simić und Predrag V. Pejović. „Passive Target Localization Problem Based on Improved Hybrid Adaptive Differential Evolution and Nelder-Mead Algorithm“. Journal of Sensors 2020 (27.02.2020): 1–20. http://dx.doi.org/10.1155/2020/3482463.

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This paper considers a passive target localization problem in Wireless Sensor Networks (WSNs) using the noisy time of arrival (TOA) measurements, obtained from multiple receivers and a single transmitter. The objective function is formulated as a maximum likelihood (ML) estimation problem under the Gaussian noise assumption. Consequently, the objective function of the ML estimator is a highly nonlinear and nonconvex function, where conventional optimization methods are not suitable for this type of problem. Hence, an improved algorithm based on the hybridization of an adaptive differential evolution (ADE) and Nelder-Mead (NM) algorithms, named HADENM, is proposed to find the estimated position of a passive target. In this paper, the control parameters of the ADE algorithm are adaptively updated during the evolution process. In addition, an adaptive adjustment parameter is designed to provide a balance between the global exploration and the local exploitation abilities. Furthermore, the exploitation is strengthened using the NM method by improving the accuracy of the best solution obtained from the ADE algorithm. Statistical analysis has been conducted, to evaluate the benefits of the proposed modifications on the optimization performance of the HADENM algorithm. The comparison results between HADENM algorithm and its versions indicate that the modifications proposed in this paper can improve the overall optimization performance. Furthermore, the simulation shows that the proposed HADENM algorithm can attain the Cramer-Rao lower bound (CRLB) and outperforms the constrained weighted least squares (CWLS) and differential evolution (DE) algorithms. The obtained results demonstrate the high accuracy and robustness of the proposed algorithm for solving the passive target localization problem for a wide range of measurement noise levels.

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Hedar, Abdel-Rahman, Amira A. Allam und Wael Deabes. „Memory-Based Evolutionary Algorithms for Nonlinear and Stochastic Programming Problems“. Mathematics 7, Nr. 11 (17.11.2019): 1126. http://dx.doi.org/10.3390/math7111126.

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In this paper, we target the problems of finding a global minimum of nonlinear and stochastic programming problems. To solve this type of problem, we propose new approaches based on combining direct search methods with Evolution Strategies (ESs) and Scatter Search (SS) metaheuristics approaches. First, we suggest new designs of ESs and SS with a memory-based element called Gene Matrix (GM) to deal with those type of problems. These methods are called Directed Evolution Strategies (DES) and Directed Scatter Search (DSS), respectively, and they are able to search for a global minima. Moreover, a faster convergence can be achieved by accelerating the evolutionary search process using GM, and in the final stage we apply the Nelder-Mead algorithm to find the global minimum from the solutions found so far. Then, the variable-sample method is invoked in the DES and DSS to compose new stochastic programming techniques. Extensive numerical experiments have been applied on some well-known functions to test the performance of the proposed methods.

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Chelouah, Rachid, und Patrick Siarry. „Genetic and Nelder–Mead algorithms hybridized for a more accurate global optimization of continuous multiminima functions“. European Journal of Operational Research 148, Nr. 2 (Juli 2003): 335–48. http://dx.doi.org/10.1016/s0377-2217(02)00401-0.

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Nersisson, Ruban, und Mathew M. Noel. „Hybrid Nelder-Mead search based optimal Least Mean Square algorithms for heart and lung sound separation“. Engineering Science and Technology, an International Journal 20, Nr. 3 (Juni 2017): 1054–65. http://dx.doi.org/10.1016/j.jestch.2017.02.005.

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Liu, Xinran, Zhongju Wang, Long Wang, Chao Huang und Xiong Luo. „A Hybrid Rao-NM Algorithm for Image Template Matching“. Entropy 23, Nr. 6 (27.05.2021): 678. http://dx.doi.org/10.3390/e23060678.

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This paper proposes a hybrid Rao-Nelder–Mead (Rao-NM) algorithm for image template matching is proposed. The developed algorithm incorporates the Rao-1 algorithm and NM algorithm serially. Thus, the powerful global search capability of the Rao-1 algorithm and local search capability of NM algorithm is fully exploited. It can quickly and accurately search for the high-quality optimal solution on the basis of ensuring global convergence. The computing time is highly reduced, while the matching accuracy is significantly improved. Four commonly applied optimization problems and three image datasets are employed to assess the performance of the proposed method. Meanwhile, three commonly used algorithms, including generic Rao-1 algorithm, particle swarm optimization (PSO), genetic algorithm (GA), are considered as benchmarking algorithms. The experiment results demonstrate that the proposed method is effective and efficient in solving image matching problems.

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Sochi, Taha. „Deterministic and stochastic algorithms for resolving the flow fields in ducts and networks using energy minimization“. International Journal of Modern Physics C 27, Nr. 04 (23.02.2016): 1650036. http://dx.doi.org/10.1142/s0129183116500364.

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Several deterministic and stochastic multi-variable global optimization algorithms (Conjugate Gradient, Nelder–Mead, Quasi-Newton and global) are investigated in conjunction with energy minimization principle to resolve the pressure and volumetric flow rate fields in single ducts and networks of interconnected ducts. The algorithms are tested with seven types of fluid: Newtonian, power law, Bingham, Herschel–Bulkley, Ellis, Ree–Eyring and Casson. The results obtained from all those algorithms for all these types of fluid agree very well with the analytically derived solutions as obtained from the traditional methods which are based on the conservation principles and fluid constitutive relations. The results confirm and generalize the findings of our previous investigations that the energy minimization principle is at the heart of the flow dynamics systems. The investigation also enriches the methods of computational fluid dynamics for solving the flow fields in tubes and networks for various types of Newtonian and non-Newtonian fluids.

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Tananaev, N. I. „Fitting sediment rating curves using regression analysis: a case study of Russian Arctic rivers“. Proceedings of the International Association of Hydrological Sciences 367 (03.03.2015): 193–98. http://dx.doi.org/10.5194/piahs-367-193-2015.

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Abstract. Published suspended sediment data for Arctic rivers is scarce. Suspended sediment rating curves for three medium to large rivers of the Russian Arctic were obtained using various curve-fitting techniques. Due to the biased sampling strategy, the raw datasets do not exhibit log-normal distribution, which restricts the applicability of a log-transformed linear fit. Non-linear (power) model coefficients were estimated using the Levenberg-Marquardt, Nelder-Mead and Hooke-Jeeves algorithms, all of which generally showed close agreement. A non-linear power model employing the Levenberg-Marquardt parameter evaluation algorithm was identified as an optimal statistical solution of the problem. Long-term annual suspended sediment loads estimated using the non-linear power model are, in general, consistent with previously published results.

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Zandavi, Seid Miad, Vera Chung und Ali Anaissi. „Multi-user Remote Lab: Timetable Scheduling Using Simplex Nondominated Sorting Genetic Algorithm“. ACM/IMS Transactions on Data Science 2, Nr. 2 (02.04.2021): 1–13. http://dx.doi.org/10.1145/3437260.

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The scheduling of multi-user remote laboratories is modeled as a multimodal function for the proposed optimization algorithm. The hybrid optimization algorithm, hybridization of the Nelder-Mead Simplex algorithm, and Non-dominated Sorting Genetic Algorithm (NSGA), named Simplex Non-dominated Sorting Genetic Algorithm (SNSGA), is proposed to optimize the timetable problem for the remote laboratories to coordinate shared access. The proposed algorithm utilizes the Simplex algorithm in terms of exploration and NSGA for sorting local optimum points with consideration of potential areas. SNSGA is applied to difficult nonlinear continuous multimodal functions, and its performance is compared with hybrid Simplex Particle Swarm Optimization, Simplex Genetic Algorithm, and other heuristic algorithms. The results show that SNSGA has a competitive performance to address timetable problems.

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Rahmat, M. Sidik Augi, und Pekik Nurwantoro. „Kajian Komputasi Algoritma Kuantum Quantum V ariational Eigensolver untuk Simulasi Molekul H2“. Jurnal Fisika Indonesia 24, Nr. 1 (07.04.2020): 17. http://dx.doi.org/10.22146/jfi.v24i1.52011.

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Telah dilakukan telaah teoritis dan komputasi mengenai algoritma kuantum variational quantum eigensolver simulasi molekul H2. Algoritma variational quantum eigensolver (VQE) adalah salah satu algoritma yang dapat diterapkan pada komputer kuantum sederhana pada masa kini dan merupakan algoritma yang cukup stabil dan efek dekoherensi. Algoritma VQE disebut sebagai hybrid quantum-classical karena sebagian algoritma dikerjakan pada komputer klasik. Prinsip dasar algoritma VQE adalah prinsip variasi, yaitu pencarian fungsi gelombang yang akan mengakibatkan energi sistem kuantum memiliki energi terendah. Fungsi gelombang dan Hamiltonan pada algoritma VQE disimulasikan dengan menggunakan gerbang-gerbang kuantum. Untuk dapat dioperasikan oleh gerbang kuantum. Hamiltonan dan fungsi gelombang pada penelitian ini menggunakan wakilan kuantisasi kedua. Penelitian ini menggunakan transformasi Jordan-Wigner dan Bravyi-Kitaev dari operator fermionik menjadi operator kubit (qubit) atau gerbang kuantum.Perhitungan atau komputasi energi sistem dilakukan menggunakan komputer kuantum, namun optimasi dilakukan pada komputer klasik menggunakan algoritma optimasi seperti Nelder-Mead, Powell dan BFGS. Penelitian ini akan mendekati fungsi gelombang sistem dengan beberapa basis fungsi dan metode, kemudian dari hasil yang diperoleh akan dilihat pendekatan seperti apa yang paling cocok untuk simulasi molekul H2. Simulasi numerik pada penelitian ini menggunakan paket pemrograman OpenFermion dan layanan komputasi awan kuantum Rigetti Computing.

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Singh, Saransh, und Marc De Graef. „Dictionary Indexing of Electron Channeling Patterns“. Microscopy and Microanalysis 23, Nr. 1 (Februar 2017): 1–10. http://dx.doi.org/10.1017/s1431927616012769.

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AbstractThe dictionary-based approach to the indexing of diffraction patterns is applied to electron channeling patterns (ECPs). The main ingredients of the dictionary method are introduced, including the generalized forward projector (GFP), the relevant detector model, and a scheme to uniformly sample orientation space using the “cubochoric” representation. The GFP is used to compute an ECP “master” pattern. Derivative free optimization algorithms, including the Nelder–Mead simplex and the bound optimization by quadratic approximation are used to determine the correct detector parameters and to refine the orientation obtained from the dictionary approach. The indexing method is applied to poly-silicon and shows excellent agreement with the calibrated values. Finally, it is shown that the method results in a mean disorientation error of 1.0° with 0.5° SD for a range of detector parameters.

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Cheng, Xiang, Su Li Wang und Shu Wu Cheng. „Application of Optimization Algorithm for Ceramic Formulations“. Advanced Materials Research 518-523 (Mai 2012): 3938–42. http://dx.doi.org/10.4028/www.scientific.net/amr.518-523.3938.

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ceramic formula; genetic algorithm; the simplex method; particle swarm optimization Abstract. The composition of ceramic materials determines its performance, so ceramic formula determines the performance of the product. The factors, such as supply of local raw materials, chemical composition, and raw material price, determine the formula. Selecting raw materials from a variety of raw materials which are consistent with the target formula and the percentage content of the chemical composition is a very important job. The chemical composition in the ceramic material is various, and the traditional method is to calculate the formula by hand. The workload is very heavy, and the results are often not accurate, and don’t meet actual requirements. By minimizing the deviation of chemical composition and mineral ingredients, the chemical and comprehensive formula optimization models of ceramic preform body were constructed. Several typical optimization algorithms were used to construct the formula model, such as particle swarm optimization, genetic algorithms and Nelder-Mead simplex method. The experimental results were presented and compared and it concluded that the particle swarm optimization algorithm is superior to the other optimization algorithms.

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Ladhari, Taoufik, Intissar Khoja, Faouzi Msahli und Anis Sakly. „Parameter identification of a reduced nonlinear model for an activated sludge process based on cuckoo search algorithm“. Transactions of the Institute of Measurement and Control 41, Nr. 12 (06.02.2019): 3352–63. http://dx.doi.org/10.1177/0142331218824384.

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Parameter identification plays a key role in systems’ modeling and control. This paper deals with a parameter identification problem for an activated sludge process used in wastewater treatment. The considered model is a nonlinear one inspired from the well-known ASM1. Nature-inspired algorithms have gained significant attention over the last years as useful means to solve parameter identification problem. The proposed approach in this paper is the cuckoo search algorithm based on both the fascinating brood parasitic behavior and the lévy flights. The advantages of this method are its simplicity and robustness, but it requires a good tuning of its parameters to have the best results. The comparison of the simulation results with the Nelder-Mead method, genetic algorithm, and particle swarm optimization proves the capability of this method to identify the model’s parameters with high precision.

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JOGLEKAR, M. M., N. RAMAKRISHNAN, SUDHAKAR INGUVA, SAMPATH K. VANIMISETTI und RYAN B. MOULLIET. „NUMERICAL IMPLEMENTATION OF POROUS COMPOSITE ELECTRODE–DEGRADATION MODEL TO STUDY THE CYCLE LIFE OF LI-ION CELL“. International Journal of Computational Materials Science and Engineering 02, Nr. 02 (Juni 2013): 1350012. http://dx.doi.org/10.1142/s2047684113500127.

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A numerical study is performed on the cyclic capacity degradation of a lithium manganese oxide (LMO) cell, under 21 different combinations of temperature and state of charge (SOC), based on the phenomenological model developed earlier. Out of the 21 sets, six are used for fitting in order to establish the degradation parameters of the model and the rest could be predicted with an average accuracy of about 90%. Two optimization algorithms (Genetic and Nelder Mead) are used and the consistency of the convergence is verified. The discussion includes sensitivity analysis of a selected set of degradation parameters. In addition, an analysis of the evolution of solid electrolyte interphase (SEI) and isolation (islanding) mechanisms under varying conditions of SOC and temperatures is performed which brings out the relative contribution of each mechanism to the overall capacity fade.

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Sarakhsi, M. Khojaste, S. M. T. Fatemi Ghomi und B. Karimi. „A new hybrid algorithm of scatter search and Nelder–Mead algorithms to optimize joint economic lot sizing problem“. Journal of Computational and Applied Mathematics 292 (Januar 2016): 387–401. http://dx.doi.org/10.1016/j.cam.2015.07.027.

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Chelouah, Rachid, und Patrick Siarry. „A hybrid method combining continuous tabu search and Nelder–Mead simplex algorithms for the global optimization of multiminima functions“. European Journal of Operational Research 161, Nr. 3 (März 2005): 636–54. http://dx.doi.org/10.1016/j.ejor.2003.08.053.

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Ur Rehman, Waheed, Xinhua Wang, Yingchun Chen, Xiaogao Yang, Zia Ullah, Yiqi Cheng und Marya Kanwal. „An active control for hydrostatic journal bearing using optimization algorithms“. Industrial Lubrication and Tribology 73, Nr. 2 (25.01.2021): 316–24. http://dx.doi.org/10.1108/ilt-07-2020-0272.

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Purpose The purpose of this paper is to improve static/dynamic characteristics of active-controlled hydrostatic journal bearing by using fractional order control techniques and optimizing algorithms. Design/methodology/approach Active lubrication has ability to overcome the unpredictable harsh environmental conditions which often lead to failure of capillary controlled traditional hydrostatic journal bearing. The research develops a mathematical model for a servo feedback-controlled hydrostatic journal bearing and dynamics of model is analyzed with different control techniques. The fractional-order PID control system is tuned by using particle swarm optimization and Nelder mead optimization techniques with the help of using multi-objective performance criteria. Findings The results of the current research are compared with previously published theoretical and experimental results. The proposed servo-controlled active bearing system is studied under a number of different dynamic situations and constraints of variable spindle speed, external load, temperature changes (viscosity) and variable bearing clearance (oil film thickness). The simulation results show that the proposed system has better performance in terms of controllability, faster response, stability, high stiffness and strong resistance. Originality/value This paper develops an accurate mathematical model for servo-controlled hydrostatic bearing with fractional order controller. The results are in excellent agreement with previously published literature. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-07-2020-0272

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Chen, Chengbin, und Ling Yu. „A hybrid ant lion optimizer with improved Nelder–Mead algorithm for structural damage detection by improving weighted trace lasso regularization“. Advances in Structural Engineering 23, Nr. 3 (15.09.2019): 468–84. http://dx.doi.org/10.1177/1369433219872434.

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Structural damage detection is the kernel technique in deploying structural health monitoring. The structural damage–detection technique using heuristic algorithms has been developed at an astounding pace over the past years. However, some existing structural damage–detection methods are prone to easily fall into the local optimum and to be unstable when they are applied to complex structures. In order to make full use of advantages of heuristic algorithms and overcome abovementioned shortcomings, a hybrid algorithm, which combines the ant lion optimizer with an improved Nelder–Mead algorithm, is proposed to solve the constrained optimization problem of complex structural damage detection. First, an objective function is established for damage identification using structural modal parameters, that is, frequencies and mode shapes. The solution to the objective function is accurately attained by a newly improved weighted trace lasso which can improve the computing performance and stability of procedure and reduce randomness of weighted coefficients. After assessing the computing performance of the proposed hybrid algorithm using three classical mathematical benchmark functions, two structural damage–detection numerical simulations and a laboratory verification are then conducted to fully assess the structural damage–detection capability of the proposed method. Meanwhile, the equivalent element stiffness-reduction model is introduced to estimate the real damage severities of cracks which are created in laboratory structures and to compare with the structural damage–detection results by the proposed method. The illustrated results show that the proposed hybrid algorithm can locate damage and quantify damage severity more accurately and stably with a good robustness to noise.

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Ramadas, Gisela C. V., Ana Maria A. C. Rocha und Edite M. G. P. Fernandes. „Testing Nelder-Mead Based Repulsion Algorithms for Multiple Roots of Nonlinear Systems via a Two-Level Factorial Design of Experiments“. PLOS ONE 10, Nr. 4 (13.04.2015): e0121844. http://dx.doi.org/10.1371/journal.pone.0121844.

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Capponi, Caterina, und Marco Ferrante. „Numerical investigation of pipe length determination in branched systems by transient tests“. Water Supply 18, Nr. 3 (05.09.2017): 1062–71. http://dx.doi.org/10.2166/ws.2017.180.

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Abstract Transients are used as a diagnostic tool for pressurized pipes due to their capabilities to acquire and transmit information about system status. To interpret such information in complex systems, models obtained by the integration of the governing equations in the frequency domain are used, since they are computationally efficient and reliable. These models do not require a regular spatial grid for integration and introduce the pipe lengths as parameters. In this paper a calibration procedure based on this particular feature is introduced, to determine a basic item of information that can be lost about the water distribution system, that is the length of the pipes. The network admittance matrix method is implemented and its numerical efficiency allows the investigation of the calibration optimization function on a regular grid in the parameter space. The calibration is tested using in series a genetic and the Nelder–Mead algorithms, considering both elastic and viscoelastic material pipes. The results of the presented numerical investigation allow some insights into the existence of the solution and into the shape of the optimization function.

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Ren, Aihong, Yuping Wang und Fei Jia. „A Hybrid Estimation of Distribution Algorithm and Nelder-Mead Simplex Method for Solving a Class of Nonlinear Bilevel Programming Problems“. Journal of Applied Mathematics 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/378568.

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We propose a hybrid algorithm based on estimation of distribution algorithm (EDA) and Nelder-Mead simplex method (NM) to solve a class of nonlinear bilevel programming problems where the follower’s problem is linear with respect to the lower level variable. The bilevel programming is an NP-hard optimization problem, for which EDA-NM is applied as a new tool aiming at obtaining global optimal solutions of such a problem. In fact, EDA-NM is very easy to be implementedsince it does not require gradients information. Moreover, the hybrid algorithm intends to produce faster and more accurate convergence. In the proposed approach, for fixed upper level variable, we make use of the optimality conditions of linear programming to deal with the follower’s problem and obtain its optimal solution. Further, the leader’s objective function is taken as the fitness function. Based on these schemes, the hybrid algorithm is designed by combining EDA with NM. To verify the performance of EDA-NM, simulations on some test problems are made, and the results demonstrate that the proposed algorithm has a better performance than the compared algorithms. Finally, the proposed approach is used to solve a practical example about pollution charges problem.

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Elizabeth de Castro Silva, Francielly, und Carlos Alberto Bavastri. „A methodology for an optimal design of physical parameters, positions, and viscoelastic materials of simple dynamic absorbers for passive vibration control“. Journal of Vibration and Control 25, Nr. 6 (10.01.2019): 1133–47. http://dx.doi.org/10.1177/1077546318817809.

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Dynamic vibration absorbers are simple mechanical devices that are attached to a structure aiming at reducing vibration levels. Designing such devices for vibration control of mechanical systems using viscoelastic materials results in low costs, easy construction, and higher efficacy due to their ability to dissipate vibration energy. In this context, the present study aims at developing a methodology for an optimal design of a set of viscoelastic dynamic absorbers considering their natural frequencies, the positions to attach them onto the structure to be controlled, and the viscoelastic materials as variables to be optimized for different working temperatures. The optimal configuration is obtained by applying a hybrid optimization technique, which uses genetic algorithms (considering continuous and discrete variables in the same design vector) aiming at approximating the global minimum point and, subsequently, a nonlinear programming method (simplex based on the Nelder–Mead method) to perform a local search. An example of dynamic absorber design to reduce vibration levels in a one-degree-of-freedom (DOF) system and on a steel plate (multiple-DOFs) is presented. The results show the efficacy of the methodology for passive control of vibrations acting on a broadband of frequencies and different temperatures.

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CHONG, CHUII KHIM, MOHD SABERI MOHAMAD, SAFAAI DERIS, MOHD SHAHIR SHAMSIR, LIAN EN CHAI und YEE WEN CHOON. „USING AN IMPROVED BEE MEMORY DIFFERENTIAL EVOLUTION ALGORITHM FOR PARAMETER ESTIMATION TO SIMULATE BIOCHEMICAL PATHWAYS“. Journal of Biological Systems 22, Nr. 01 (März 2014): 101–21. http://dx.doi.org/10.1142/s0218339014500065.

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When analyzing a metabolic pathway in a mathematical model, it is important that the essential parameters are estimated correctly. However, this process often faces few problems like when the number of unknown parameters increase, trapping of data in the local minima, repeated exposure to bad results during the search process and occurrence of noisy data. Thus, this paper intends to present an improved bee memory differential evolution (IBMDE) algorithm to solve the mentioned problems. This is a hybrid algorithm that combines the differential evolution (DE) algorithm, the Kalman filter, artificial bee colony (ABC) algorithm, and a memory feature. The aspartate and threonine biosynthesis pathway, and cell cycle pathway are the metabolic pathways used in this paper. For three production simulation pathways, the IBMDE managed to robustly produce the estimated optimal kinetic parameter values with significantly reduced errors. Besides, it also demonstrated faster convergence time compared to the Nelder–Mead (NM), simulated annealing (SA), the genetic algorithm (GA) and DE, respectively. Most importantly, the kinetic parameters that were generated by the IBMDE have improved the production rates of desired metabolites better than other estimation algorithms. Meanwhile, the results proved that the IBMDE is a reliable estimation algorithm.

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Luangpaiboon, Pongchanun, und Sitthikorn Duangkaew. „Artificial Intelligence Mechanisms on Interactive Modified Simplex Method with Desirability Function for Optimising Surface Lapping Process“. Mathematical Problems in Engineering 2014 (2014): 1–16. http://dx.doi.org/10.1155/2014/864586.

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A study has been made to optimise the influential parameters of surface lapping process. Lapping time, lapping speed, downward pressure, and charging pressure were chosen from the preliminary studies as parameters to determine process performances in terms of material removal, lap width, and clamp force. The desirability functions of the-nominal-the-best were used to compromise multiple responses into the overall desirability function level orDresponse. The conventional modified simplex or Nelder-Mead simplex method and the interactive desirability function are performed to optimise online the parameter levels in order to maximise theDresponse. In order to determine the lapping process parameters effectively, this research then applies two powerful artificial intelligence optimisation mechanisms from harmony search and firefly algorithms. The recommended condition of (lapping time, lapping speed, downward pressure, and charging pressure) at (33, 35, 6.0, and 5.0) has been verified by performing confirmation experiments. It showed that theDresponse level increased to 0.96. When compared with the current operating condition, there is a decrease of the material removal and lap width with the improved process performance indices of 2.01 and 1.14, respectively. Similarly, there is an increase of the clamp force with the improved process performance index of 1.58.

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Liu, Jiahao, Yuze Chen, Lin Xu, Rong Kong, Peng Liu und Xin Zhou. „Generalized optical design and optimization of multipass cells with independent circle patterns based on the Monte Carlo and Nelder-Mead simplex algorithms“. Optics Express 29, Nr. 13 (14.06.2021): 20250. http://dx.doi.org/10.1364/oe.429953.

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Kim, Hyungyu, Kwansu Kim, Carlo Bottasso, Filippo Campagnolo und Insu Paek. „Wind Turbine Wake Characterization for Improvement of the Ainslie Eddy Viscosity Wake Model“. Energies 11, Nr. 10 (19.10.2018): 2823. http://dx.doi.org/10.3390/en11102823.

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This paper presents a modified version of the Ainslie eddy viscosity wake model and its accuracy by comparing it with selected exiting wake models and wind tunnel test results. The wind tunnel test was performed using a 1.9 m rotor diameter wind turbine model operating at a tip speed ratio similar to that of modern megawatt wind turbines. The control algorithms for blade pitch and generator torque used for below and above rated wind speed regions similar to those for multi-MW wind turbines were applied to the scaled wind turbine model. In order to characterize the influence of the wind turbine operating conditions on the wake, the wind turbine model was tested in both below and above rated wind speed regions at which the thrust coefficients of the rotor varied. The correction of the Ainslie eddy viscosity wake model was made by modifying the empirical equation of the original model using the wind tunnel test results with the Nelder-Mead simplex method for function minimization. The wake prediction accuracy of the modified wake model in terms of wind speed deficit was found to be improved by up to 6% compared to that of the original model. Comparisons with other existing wake models are also made in detail.

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Rasmy, Laila, Imane Sebari und Mohamed Ettarid. „Automatic Sub-Pixel Co-Registration of Remote Sensing Images Using Phase Correlation and Harris Detector“. Remote Sensing 13, Nr. 12 (12.06.2021): 2314. http://dx.doi.org/10.3390/rs13122314.

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In this paper, we propose a new approach for sub-pixel co-registration based on Fourier phase correlation combined with the Harris detector. Due to the limitation of the standard phase correlation method to achieve only pixel-level accuracy, another approach is required to reach sub-pixel matching precision. We first applied the Harris corner detector to extract corners from both references and sensed images. Then, we identified their corresponding points using phase correlation between the image pairs. To achieve sub-pixel registration accuracy, two optimization algorithms were used. The effectiveness of the proposed method was tested with very high-resolution (VHR) remote sensing images, including Pleiades satellite images and aerial imagery. Compared with the speeded-up robust features (SURF)-based method, phase correlation with the Blackman window function produced 91% more matches with high reliability. Moreover, the results of the optimization analysis have revealed that Nelder–Mead algorithm performs better than the two-point step size gradient algorithm regarding localization accuracy and computation time. The proposed approach achieves better accuracy than 0.5 pixels and outperforms the speeded-up robust features (SURF)-based method. It can achieve sub-pixel accuracy in the presence of noise and produces large numbers of correct matching points.

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Izci, Davut. „Design and application of an optimally tuned PID controller for DC motor speed regulation via a novel hybrid Lévy flight distribution and Nelder–Mead algorithm“. Transactions of the Institute of Measurement and Control 43, Nr. 14 (15.06.2021): 3195–211. http://dx.doi.org/10.1177/01423312211019633.

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This paper deals with the design of an optimally performed proportional–integral–derivative (PID) controller utilized for speed control of a direct current (DC) motor. To do so, a novel hybrid algorithm was proposed which employs a recent metaheuristic approach, named Lévy flight distribution (LFD) algorithm, and a simplex search method known as Nelder–Mead (NM) algorithm. The proposed algorithm (LFDNM) combines both LFD and NM algorithms in such a way that the good explorative behaviour of LFD and excellent local search capability of NM help to form a novel hybridized version that is well balanced in terms of exploration and exploitation. The promise of the proposed structure was observed through employment of a DC motor with PID controller. Optimum values for PID gains were obtained with the aid of an integral of time multiplied absolute error objective function. To verify the effectiveness of the proposed algorithm, comparative simulations were carried out using cuckoo search algorithm, genetic algorithm and original LFD algorithm. The system behaviour was assessed through analysing the results for statistical and non-parametric tests, transient and frequency responses, robustness, load disturbance, energy and maximum control signals. The respective evaluations showed better performance of the proposed approach. In addition, the better performance of the proposed approach was also demonstrated through experimental verification. Further evaluation to demonstrate better capability was performed by comparing the LFDNM-based PID controller with other state-of-the-art algorithms-based PID controllers with the same system parameters, which have also confirmed the superiority of the proposed approach.

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Rahimi, Iman, Amir H. Gandomi, Panagiotis G. Asteris und Fang Chen. „Analysis and Prediction of COVID-19 Using SIR, SEIQR, and Machine Learning Models: Australia, Italy, and UK Cases“. Information 12, Nr. 3 (03.03.2021): 109. http://dx.doi.org/10.3390/info12030109.

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The novel coronavirus disease, also known as COVID-19, is a disease outbreak that was first identified in Wuhan, a Central Chinese city. In this report, a short analysis focusing on Australia, Italy, and UK is conducted. The analysis includes confirmed and recovered cases and deaths, the growth rate in Australia compared with that in Italy and UK, and the trend of the disease in different Australian regions. Mathematical approaches based on susceptible, infected, and recovered (SIR) cases and susceptible, exposed, infected, quarantined, and recovered (SEIQR) cases models are proposed to predict epidemiology in the above-mentioned countries. Since the performance of the classic forms of SIR and SEIQR depends on parameter settings, some optimization algorithms, namely Broyden–Fletcher–Goldfarb–Shanno (BFGS), conjugate gradients (CG), limited memory bound constrained BFGS (L-BFGS-B), and Nelder–Mead, are proposed to optimize the parameters and the predictive capabilities of the SIR and SEIQR models. The results of the optimized SIR and SEIQR models were compared with those of two well-known machine learning algorithms, i.e., the Prophet algorithm and logistic function. The results demonstrate the different behaviors of these algorithms in different countries as well as the better performance of the improved SIR and SEIQR models. Moreover, the Prophet algorithm was found to provide better prediction performance than the logistic function, as well as better prediction performance for Italy and UK cases than for Australian cases. Therefore, it seems that the Prophet algorithm is suitable for data with an increasing trend in the context of a pandemic. Optimization of SIR and SEIQR model parameters yielded a significant improvement in the prediction accuracy of the models. Despite the availability of several algorithms for trend predictions in this pandemic, there is no single algorithm that would be optimal for all cases.

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Nawaz, M., A. Zeeshan, R. Ellahi, S. Abbasbandy und Saman Rashidi. „Joules and Newtonian heating effects on stagnation point flow over a stretching surface by means of genetic algorithm and Nelder-Mead method“. International Journal of Numerical Methods for Heat & Fluid Flow 25, Nr. 3 (07.04.2015): 665–84. http://dx.doi.org/10.1108/hff-04-2014-0103.

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Purpose – The purpose of this paper is to study the Joules heating effects on stagnation point flow of Newtonian and non-Newtonian fluids over a stretching cylinder by means of genetic algorithm (GA). The main emphasis is to find the analytical and numerical solutions for the said mathematical model. The work undertaken is a blend of numerical and analytical studies. Effects of active parameters such as: Hartmann number, Prandtl number, Eckert number, Nusselt number, Skin friction and dimensionless fluids parameters on the flow and heat transfer characteristics have been examined by graphs and tables. Compression is also made with the existing benchmark results. Design/methodology/approach – Analytical solutions of non-linear coupled equations are developed by optimal homotopy analysis method (OHAM). A very effective and higher order numerical scheme hybrid GA and Nelder-Mead optimization Algorithms are used for numerical investigations. Findings – An excellent agreement with the existing results in limiting sense is noted. It is observed that the radial velocity is an increasing function of dimensionless material parameters α 1, α 2 and β. Temperature increases by increasing the values of M, Pr, Ec and γ. Non-Newtonian parameter β has similar effects on skin friction coefficient and Nusselt number. The wall heat transfer rate is a decreasing function of A and ß whereas it increases by increasing conjugate parameter γ. Originality/value – The problem under consideration has been widely studied by many investigators due to its importance and engineering applications. But most of the studies as the authors have documented are for Newtonian or viscous fluids. But no such analysis is available in the literature which can describe the Joules heating effects on stagnation point flow of Newtonian and non-Newtonian fluids over a stretching cylinder by means of GA.

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